Problem: As you very well know, this year's funkiest numbers are so called triangular numbers (that is, integers that are representable as <image>, where k is some positive integer), and the coolest numbers are those that are representable as a sum of two triangular numbers.

A well-known hipster Andrew adores everything funky and cool but unfortunately, he isn't good at maths. Given number n, help him define whether this number can be represented by a sum of two triangular numbers (not necessarily different)!

Input

The first input line contains an integer n (1 ≤ n ≤ 109).

Output

Print "YES" (without the quotes), if n can be represented as a sum of two triangular numbers, otherwise print "NO" (without the quotes).

Examples

Input

256


Output

YES


Input

512


Output

NO

Note

In the first sample number <image>.

In the second sample number 512 can not be represented as a sum of two triangular numbers.

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;
int main() {
  ios_base::sync_with_stdio(0);
  cin.tie(0);
  cout.tie(0);
  ;
  vector<long long int> v;
  map<long long int, bool> mp;
  for (long long int i = 1;; i++) {
    long long int num = (i * (i + 1)) / 2;
    v.push_back(num);
    mp[num] = 1;
    if (num > 1e9) break;
  }
  long long int n, x, y, z;
  cin >> n;
  x = v.size();
  for (int i = 0; i < x; i++) {
    long long int num;
    if (v[i] < n) {
      num = n - v[i];
      if (mp[num]) {
        cout << "YES\n";
        return 0;
      }
    } else {
      break;
    }
  }
  cout << "NO\n";
}